A245351 Sum of digits of n written in fractional base 10/7.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 21, 22, 23, 24, 25, 26, 27, 28

Offset

0,3

Comments

The base 10/7 expansion is unique and thus the sum of digits function is well-defined.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for sequences related to fractional bases.

Formula

a(n) = A007953(A024662(n)).

Example

In base 10/7 the number 14 is represented by 74 and so a(14) = 7 + 4 = 11.

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[7 * Floor[n/10]] + Mod[n, 10]]; Array[a, 100, 0] (* Amiram Eldar, Aug 04 2025 *)

Prog

(SageMath) # uses [basepqsum from A245355]
[basepqsum(10, 7, w) for w in [0..200]]
(PARI) a(n) = if(n == 0, 0, a(n\10 * 7) + n % 10); \\ Amiram Eldar, Aug 04 2025

Crossrefs

Cf. A000120, A007953, A024662, A244040.

Sequence in context: A328469 A373229 A347105 * A028902 A081598 A390503

Adjacent sequences: A245348 A245349 A245350 * A245352 A245353 A245354

Keyword

nonn,base,easy

Author

Hailey R. Olafson, Jul 18 2014

Status

approved